Tests for relation type - equivalence or tolerance - in a finite set of elements
Tests in weakly nonlinear regression model
In weakly nonlinear regression model a weakly nonlinear hypothesis can be tested by linear methods if an information on actual values of model parameters is at our disposal and some condition is satisfied. In other words we must know that unknown parameters are with sufficiently high probability in so called linearization region. The aim of the paper is to determine this region.
The application of minimax fit in linear model and its extension in generalised linear models.
The Bayes estimator of the variance components and its admissibility
The Bias of Least Squares Polynomial Interpolants.
The closeness of the range of a probability on a certain system of random events -- an elementary proof.
The correloid
The cross-validation method in the polynomial regression.
The Determination of Expected Mean Squares for Anova in Balanced Designs.
The effect of a single point on correlation and slope.
The efficiency of modified jackknife and ridge type regression estimators: a comparison.
The expected variation of random bounded integer sequences of finite length.
The Frisch scheme in algebraic and dynamic identification problems
This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension...
The full rank case for a linearizable model.
The generalized p-point method of estimation of regression coefficients
The Generalized Ridge Estimator and Improved Adjustments for Regression Parameters
The LASSO estimator: Distributional properties
The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO estimator, but it is also well-known that the asymptotic results can give a wrong picture of the LASSO estimator's actual finite-sample behaviour. The finite sample distribution of the LASSO estimator has been previously studied for the special case of orthogonal models....
The least trimmed squares. Part I: Consistency
The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [HamRonRouSta]) is proved under general conditions. The assumptions employed in paper are discussed in details to clarify the consequences for the applications.
The least trimmed squares. Part II: -consistency
-consistency of the least trimmed squares estimator is proved under general conditions. The proof is based on deriving the asymptotic linearity of normal equations.
The least trimmed squares. Part III: Asymptotic normality
Asymptotic normality of the least trimmed squares estimator is proved under general conditions. At the end of paper a discussion of applicability of the estimator (including the discussion of algorithm for its evaluation) is offered.